Lesson 6.1: Systems of Linear Equations and Inequalities

Question 1

System of Linear Equations

Answer 1

consists of two or more linear equations with the same variables

Question 2

Linear Inequality

Answer 2

A linear inequality in two variables takes the form y>mx+b or y<mx+b. (You can also use the ≤ or ≥
signs.) Linear inequalities are closely related to graphs of straight lines; recall that a straight line has the equation y=mx+b.

Question 3

Half Plane

Answer 3

When a linear equation is graphed in a coordinate plane, the line splits the plane into two pieces. Each piece is called a half plane.

Question 4

Boundary Line

Answer 4

y=mx+b (separates the coordinate plane)

Question 5

Solution Set

Answer 5

shown by shading/coloring the half plane

Question 6

Dashed Line

Answer 6

For a strict inequality (< or >), we draw a dashed line to show that the points in the line are not part of the solution.

Question 7

Test Point

Answer 7

A point that you choose to substitute into your inequality to check whether or not this point makes a true inequality or not. If the inequality is TRUE when the test point is substituted in, then you’ll shade on the side of that point. If it is NOT TRUE then you shade on the other side of the line from that point

Question 8

Cartesian grid

Answer 8

Coordinate plan (to graph functions)

Question 9

Coincide

Answer 9

are the same

Question 10

Coincide

Answer 10

are the same

Question 11

Solid Line

Answer 11

If the signs ≤ or ≥ are present then a solid line will be drawn.

Question 12

Solid Line

Answer 12

If the signs ≤ or ≥ are present then a solid line will be drawn.

Question 13

Solid Line

Answer 13

For an inequality that includes the equals sign (≤ or ≥), we draw a solid line to show that the points on the line are part of the solution.

Question 14

Unbounded Region

Answer 14

Shaded area of Systems of Linear Inequalities (2 lines and they’re shading overlaps) continues forever in at least one direction